October 20, 1985|Robert Kanigel | Kanigel's book about elite scientists and their mentors is to be published by Macmillan next fall. and

What is the irreducible essence, the soul or spirit, of the letter 'A'? Within that seemingly Talmudic question lies much of the terrain that Douglas Hofstadter explores in "Metamagical Themas"--the fuzzy borders between mind and machine, animate and inanimate, creative and mechanical. Humans fancy their minds as something higher and better than a bunch of computer chips mechanistically chugging along. But if so, what is that elusive something extra?

In 1980, the year following publication of "Godel, Escher, Bach: An Eternal Golden Braid," his Pulitzer Prize-winning foray into the realm of symbol, form, meaning and mind, Hofstadter was asked by the editors of Scientific American to take over the "Mathematical Games" column long presided over by Martin Gardner. (In a characteristic twist, Hofstadter named his column "Metamagical Themas"--an anagram on the original title.) By July, 1983, he'd written 25 of the columns, all of which are here collected and patched together with additional articles, introductions, post scripts, bibliographical notes, personal acknowledgements and asides.

As in his endlessly inventive first book, Hofstadter reaches beyond the traditional essay form and includes fanciful dialogues, programming sequences, poems, game rules, excerpts from personal letters, comic strips and more. The topics he addresses are similarly varied, ranging from Rubik's Cube, the genetic code, foreign-language translation, typefaces and computer games to Heisenberg's Uncertainty Principle and the music of Frederic Chopin.

Yet this is no mere collection of random essays. Behind it all lurks Hofstadter's "home" field, artificial intelligence, universally known as AI, and his own playful, occasionally self-indulgent, frequently brilliant intellect. Hofstadter has much to say; it's all of a piece, and his disquisitions on the letter 'A' are at the heart of it.

As he demonstrates with a page of 'A's plucked from a standard typeface catalogue, "pointed top with horizontal crossbar" fails utterly in defining 'A'; numerous highly styled exceptions little resemble the block 'A's of first grade while yet being instantly and unambiguously recognizable by any reader of the Latin alphabet. They elude recognition, however, by even the biggest computers.

"The shape of a letter form is a surface manifestation of deep mental abstractions," argues Hofstadter. We're hardly apt to reach an understanding of the mind, says he, if what no computer can do and virtually every literate human can, resists analysis. As long as it does, getting a computer to exhibit anything like human intelligence will remain elusive.

Human creativity can't be reduced to neat, crisp, formal correspondence between this and that, that and this, Hofstadter argues. Rather, its distinguishing feature is what he calls "slippability"--a sense of metaphor, of this as like that rather than this is exactly that, of a rigid, mechanical grinding of gears giving way to easy fluid swirls.

Pulling most irresistibly on Hofstadter's imagination is how worlds of beauty, grace and elegant complexity can emerge from mechanical and "uncreative" roots. Like "parquet" designs--fields of squares reminiscent of parquet flooring progressively distorted by simple computer instructions that yield exquisite designs. Or, for that matter, life itself, with all its rich variation, built up from only four DNA nucleotides.

That quantum mechanics, say, gives wildly counterintuitive answers to our questions about physical reality is not surprising, says Hofstadter. Probe any reality and we rightly demand answers that go beyond our original question: What makes a brick solid? To say it's composed of zillions of micro-bricks is hardly illuminating. Writes Hofstadter: "What we ultimately want is for solidity to vanish, to dissolve, to disintegrate into some totally different kind of phenomenon with which we have no experience."

The same goes for creativity, consciousness, mind: We shouldn't expect to find some little guy up there being "creative." Rather, there's something else at work entirely--something that for Hofstadter is wrapped up in the nature of pattern and form.

"Systems that are not interfaced with our tangible, three-dimensional world via perceptors and motor capacities, no matter how sophisticated their innards, seem to be unidentifiable-with, by most people." Ordinarily, language like that is properly relegated to the scrapheap of academic unreadability. Hofstadter, though, gets away with it. Just as he does with his incessant wordplay--which, while eight parts delight, is also two parts annoyance. Because such failings are redeemed by the fact that, page after page, for more than 800, Douglas Hofstadter is interesting . He does not write prose good enough to rescue stale ideas; but his ideas are so good and so many they need no rescue.

Not that he has magically alchemized abstract mathematics into some sort of page-turning thriller; "Metamagical Themas" demands work, tolerance for abstraction, and fondness for ideas. And there are times, especially in Hofstadter's three-essay treatise on the AI language called LISP, when the reader may feel inclined, as I did, to throw up his hands in frustration.

Still, Hofstadter makes the concerns of a small coterie of mathematicians, philosophers, computer scientists, and cognitive psychologists matter to those who might not otherwise care to fret over them. His is a deeply felt piece of work, even passionate in its way, that leaves us seduced by the enigma of creativity and intelligence.